This talk is based on joint work with Sungkyung Kang and JungHwan Park. We show that the (2n,1)-cable of the figure-eight knot has infinite order in the smooth concordance group, for any n≥1. The proof relies on the real κ-invariant, which satisfies a real version of the 10/8-inequality, in combination with techniques involving higher-order branched covers of knots and surfaces. Together with earlier work by Hom, Kang, Park, and Stoffregen, this result implies that any nontrivial cable of the figure-eight knot has infinite order in the smooth concordance group.

In the 1980s, Thurston introduced a new (asymmetric) metric on Teichmüller space based on best Lipschitz maps between two homeomorphic hyperbolic surfaces, instead of quasi-conformal maps which are used in the original theory of Teichmüller. In this series of lectures, I will explain his theory and discuss recent progress in the field. Three lectures will cover the following topics, but I may also add other materials. (1) General theory of Thurston’s asymmetric metric (2) Geodesics with respect to Thurston’s metric (3) Infinitesimal structures of Teichmüller space with Thurston’s metric

In the 1980s, Thurston introduced a new (asymmetric) metric on Teichmüller space based on best Lipschitz maps between two homeomorphic hyperbolic surfaces, instead of quasi-conformal maps which are used in the original theory of Teichmüller. In this series of lectures, I will explain his theory and discuss recent progress in the field. Three lectures will cover the following topics, but I may also add other materials. (1) General theory of Thurston’s asymmetric metric (2) Geodesics with respect to Thurston’s metric (3) Infinitesimal structures of Teichmüller space with Thurston’s metric

In the 1980s, Thurston introduced a new (asymmetric) metric on Teichmüller space based on best Lipschitz maps between two homeomorphic hyperbolic surfaces, instead of quasi-conformal maps which are used in the original theory of Teichmüller. In this series of lectures, I will explain his theory and discuss recent progress in the field. Three lectures will cover the following topics, but I may also add other materials. (1) General theory of Thurston’s asymmetric metric (2) Geodesics with respect to Thurston’s metric (3) Infinitesimal structures of Teichmüller space with Thurston’s metric